Finite Group Databasebeta

← #30608397

Subgroups — #30608397

Order 15616.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462092C212yesmaximal
2#21460960C214yesmaximal, complemented
3#21456220C211yesmaximal, characteristic
4#16840741—22no—
5#16840669—22no—
6#16840667C2214yes—
7#16840312C2211yescharacteristic
8C2×#14519769C411yescharacteristic, complemented
9#16840131C412yescomplemented
10#16840127C2212yes—
11#16840117—22no—
12#16839764—22no—
13C4×M16×C61C411yescharacteristic, complemented
14#14519856—42no—
15#14519836—24no—
16#14519835—42no—
17C2×#11758222D412yes—
18#14519777C2×C411yescharacteristic
19#14519774C2311yescharacteristic
20#14519769—21no—
21#14519769—41no—
22#14519769C2×C412yes—
23#14519765D412yes—
24#14519751—41no—
25C4×D244—41no—
26C2×C4⋊Dic61—21no—
27C2×#11758196—41no—
28#14519702—24no—
29#14519699—24no—
30C2×M16×C61—21no—
31C2×C42×C61C2×C411yescharacteristic
32#97×C61C2×C412yes—
33C4×C8×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C22⋊C411yescharacteristic
36C2×C22⋊D61—22no—
37C22×Dic61—41no—
38#11758222—42no—
39#11758222—42no—
40C2×D244—41no—
41C2×D244C2×D412yes—
42C2×C4×D61—22no—
43C2×Dic122C22⋊C412yes—
44C22⋊#6923—44no—
45C4⋊#6923—82no—
46C4×#6923—82no—
47M16×C61—42no—
48C2×C8×C61—22no—
49C42×C61—21no—
50C42×C61C22⋊C411yescharacteristic
51C42×C61C22×C411yescharacteristic
52#11758198—42no—
53C4⋊Dic61—22no—
54C4⋊Dic61—41no—
55C4⋊Dic61—41no—
56#11758196—42no—
57#11758196—42no—
58C23×C61#9911yescharacteristic
59C22×D61—22no—
60C2×#6923—84no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—81no—
65C2×C4×C61#9911yescharacteristic
66C2×C4×C61C2×C22⋊C411yescharacteristic
67C22⋊D61—82no—
68C2×Dic61—22no—
69C2×Dic61—42no—
70C2×Dic61—82no—
71D244—42no—
72D244—82no—
73C4×D61—42no—
74C4×D61—42no—
75Dic122—42no—
76C8×C61—42no—
77#13596—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—41no—
80C22×C61C2×#9911yescharacteristic
81C2×D61—42no—
82C2×D61—82no—
83#6923—164no—
84C4×C61—21no—
85C4×C61—41no—
86C4×C61—41no—
87C4×C61#35412yes—
88Dic61—42no—
89Dic61—82no—
90#3142—611no—
91#2126—612no—
92#1412—614no—
93C2×C61—21no—
94C2×C61—41no—
95C2×C61C2×#35411yescharacteristic
96D61—82no—
97#532—611no—
98C2×#125—611no—
99#491—612no—
100#490—612no—
101#488—1222no—
102#417—1222no—
103#410—1222no—
104C4×M16#692311yescharacteristic, complemented
105#354—1222no—
106#353—614no—
107C61#1359611yescharacteristic, complemented, Sylow
108C2×#41—612no—
109C2×M16—21no—
110C4⋊Q8—611no—
111#127—611no—
112#125—612no—
113#125—1221no—
114#125—2441no—
115#124—612no—
116#121—2441no—
117C4×D4—2441no—
118#117—2442no—
119C2×C4⋊C4—1221no—
120C2×C4⋊C4—2441no—
121C2×C42C2×#692311yescharacteristic
122#103—1224no—
123#102—1224no—
124#99—1224no—
125#99—2442no—
126#97C2×#692312yes—
127C4×C8—21no—
128#41—2442no—
129#41—2442no—
130C2×Q8—612no—
131C2×D4—612no—
132C2×D4—1222no—
133C2×D4—2441no—
134C22×C4—21no—
135C22×C4—1222no—
136C22×C4—2441no—
137C22×C4C22⋊#692311yescharacteristic
138M16—42no—
139C2×C8—22no—
140C4⋊C4—1222no—
141C4⋊C4—4882no—
142C4⋊C4—2441no—
143C4⋊C4—2442no—
144C4⋊C4—2442no—
145C4⋊C4—2441no—
146C22⋊C4—2442no—
147C22⋊C4—2444no—
148C42—21no—
149C42—4882no—
150C42C22⋊#692311yescharacteristic
151C42C22×#692311yescharacteristic
152C23—1222no—
153C23#1451983611yescharacteristic
154Q8—2442no—
155D4—4882no—
156D4—4882no—
157D4—2442no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—81no—
162C2×C4—1222no—
163C2×C4—4884no—
164C2×C4—4882no—
165C2×C4—2442no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4#1451983611yescharacteristic
169C2×C4C2×C22⋊#692311yescharacteristic
170C8—42no—
171C22—21no—
172C22—41no—
173C22—4882no—
174C22—2442no—
175C22C2×#1451983611yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—9764no—
180C4—4882no—
181C4—2442no—
182C4#1684066912yes—
183C2—21no—
184C2—41no—
185C2—4882no—
186C2C2×#1684066911yescharacteristic
subgroupG/H
centerC2C2×#16840669
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC4×M16×C61C4
socleC2×C61C2×#354
prime radical#16840312C22
cosocle#14519774C23
hypercenterC4×M16#6923
hypocenterC61#13596
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21460960C2semidirect
8. C2×#14519769C4semidirect
9. #16840131C4semidirect
13. C4×M16×C61C4semidirect
104. C4×M16#6923semidirect
107. C61#13596semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214620922
#214609602
#214562202
#1359661